Question: How to determine area under the curve resulting from a dsolve graph?

Hi everyone,

I am having trouble determining how to obtain the area under the curve of a "complex" dsolve graph, as an example:

> restart;
> with(plots);
> g := diff(S(t), t) = t^2;
> q := diff(R(t), t) = t;
> ode1 := dsolve([g, S(0) = 1, q, R(0) = 1], [S(t), R(t)], numeric, events = [[t = 600, S(t) = 10^7], [t = 800, S(t) = 5*10^7]]);
> odeplot(ode1, [t, S(t)+R(t), color = blue, thickness = 2], 0 .. 1000, numpoints = 1000); 

Let's say that I would like to determine the area under the curve of S(t)+R(t) versus t, between t=0 and t=1000. The graph could be divided into sections as determined by the events markers in the above example, but I'm still not sure how to integrate this kind of function in Maple.

Any help would be appreciated!

Thanks in advance


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